“When I was young, I thought these people were angels and we had to follow them,” said Mr Bawardi, formerly Inmate 68 at Guantanamo and one of hundreds of Saudi al Qaeda suspects arrested after the US invasion of Afghanistan. “Now, though, I can see between right and wrong.”

Quietly-spoken, and dressed in a traditional Arab robe and keffiya, Mr Bawardi is an alumnus of the Prince Mohammed bin Nayef Centre for Counselling and Care outside Riyadh, where for the last two years, batches of former Guantanamo inmates have undergone religious “deprogramming” in exchange for their liberty.

With its swimming pool, games rooms and therapy courses such as “10 Steps Toward Positive Thinking”, it resembles a jihadist’s version of London’s Priory clinic. Yet like any rehab programme, it also has its recidivists – and Batch 10, to which Mr Bawardi belonged, is a case in point.

The tenth group of Saudis to be flown back from Guantanamo Bay, no less than five of the original 14 who passed through the programme absconded to neighbouring Yemen to re-embrace terrorism. To the embarrassment of their mentors, and the dismay of Washington, one Batch 10 member, Said al-Shihri, has since re-surfaced as no less than deputy leader of al-Qaeda in the Arabian Peninsula, the movement’s new Yemen-based branch. The group opened up the latest frontier in the war on terror last month, when it claimed to have groomed the so-called Detroit “Underpants Bomber”, Umar Farouk Abdulmutallab.

Such “relapses” show how, more than eight years since 9-11, al-Qaeda has confounded its doomsayers with both its resilience and its ever-spreading presence.

When Batch 10 first arrived back at Riyadh airport two years ago, Western diplomats and intelligence officials were becoming increasingly confident that the movement was on its back foot.

In Iraq, it had suffered a major revolt from its allies in the Sunni Muslim insurgency, amid revulsion at tactics like indiscriminate suicide bombings and sectarian killing. In Europe and America, its failure to unleash any kind of “spectacular” since the July 2005 London bombings had diminished its capability to inspire new volunteers. And in Pakistan and Afghanistan, US airstrikes against al-Qaeda’s upper ranks meant that the few would-be recruits who did still go there complained of poor leadership and lack of training.

As Western intelligence officers gleefully noted, some even went home disillusioned. When a newly-installed Barack Obama ordered Guantanamo Bay to be shut down, the hope was that it might also herald the closure of the al-Qaeda era altogether.

Last week, though, as diplomats gathered in London for crisis meetings on the future of both Afghanistan and Yemen, the mood was rather less upbeat. Like a global franchise, outlets of the movement have begun baring their teeth throughout a giant arc across Africa and the Middle East, finding new homes in places where the writ of government is weak or non-existent.

In the Sahara and north Africa, militants blooded in Iraq have formed al-Qaeda in the Islamic Magreb, kidnapping diplomats, aid workers and tourists including the Briton, Edwin Dyer, who was murdered last year.

In pirate-infested Somalia, where no central government has existed for nearly 20 years, the movement’s spiritual cousins, the al-Shabaab movement, are now the only effective authority in the south. In Pakistan and Iraq, it continues to strike despite huge security operations – last week, suicide bombers killed 40 people in Baghdad.

And on the outer rims of the Muslim world, from war-ravaged Chechnya to mountainous Tajikistan and beyond, its operatives come and go – on Wednesday, 10 people suspected of links to the Yemen faction were arrested in Malaysia. Meanwhile, Osama bin Laden remains as free as ever somewhere in the tribal badlands of the Afghanistan-Pakistan border, and Mr Obama has decided to halt the release of further Guantanamo Bay inmates back to Yemen.

American analysts liken the military battle against al-Qaeda to the fairground game of Whack-a-Mole: bash the offending animal on the head in one hole and it simply pops up out of another.

“Seventy-five per cent of the plots we uncover are linked towards Pakistan, but Somalia and Yemen are also now becoming a major concern,” said one serving M15 officer. “Al-Qaeda now has a foothold in every Arab country in the Middle East, as well as Chechnya. There is also the threat from terrorists who self-radicalise and have no connection with any group.”

Of greatest immediate concern is Yemen, where the Detroit bomber is believed to have joined scores of foreign jihadists receiving specialised training for operations in the West. The ancestral home of the Bin Laden family before they moved north to Saudi Arabia, the rugged, poverty-stricken nation is a prime contender to become another Afghanistan. Its government is notoriously weak and corrupt, and its security forces exercise little writ over a gun-loving population of 20 million that own some 60 million weapons but little else.

In the dirt-poor, inaccessible mountain regions, al-Qaeda finds it easy to buy protection from local tribes, who often resent Yemen’s Western-backed government as much as they do. And with nationwide unemployment at 40 per cent and rising, there is no shortage of idle hands for whom the movement may find work – at roundabouts in the ancient capital, Sana’a, any foreign car that stops attracts a horde of men hoping to be hired as day labourers. Security officials are now also braced for a further influx of would-be jihadists following the publicity garnered by the Detroit attack.

“Everything points to Yemen replacing Afghanistan and Iraq as the destination of choice for foreign Muslims wanting to wage jihad,” said Saeed Ali al-Jemhi, a Yemeni expert on al-Qaeda’s local affiliate.

One European diplomat observed. “What we may be seeing now is disparate groups across East Africa, the Horn and into the Arabian Peninsula starting to join together properly for the first time.”

Certainly, across the Gulf of Aden in Somalia, al-Shabaab has rolled out the welcome mat for fighters from Europe, America and the Middle East, adding to what are already swelling ranks of local recruits.

While the Somalis have traditionally followed a moderate strain of Sufi Islam, the growth of an entire generation who have known nothing but fighting has created a more receptive atmosphere to religious fanaticism. Al-Shabaab has also offered to send fighters to Yemen if needed, and while it publicly disavows piracy, Western officials believe it is only a matter of time before it wakes up to the possibilities of attacking shipping in the Gulf of Aden.

Many of the key figures in al-Qaeda’s newer strongholds have personal links to the core leadership around Bin Laden. Mukhtar Abu Zubayr, al-Shabaab’s most influential commander, fought against the Soviets in Afghanistan at the same time, while Nasir al-Wahayshi, al-Qaeda’s No 1 in Yemen, once served as Bin Laden’s secretary. What makes them so hard to defeat, however, is not their ability to unite and cooperate but their ability to divide and operate independently.

“Obama might have made the mistake of tying the battle against al-Qaeda to Afghanistan, when it was always likely to spread in the next 18 months,” said one Nato official at last week’s Afghan conference in London. “Our commanders expect any success in Afghanistan to mean that al-Qaeda just spreads to the likes of Yemen and Somalia.”

“All operations are locally planned and implemented,” said Mohammed al-Ahmadi, a Yemeni journalist who covers al-Qaeda in the Arab Peninsula. “There may be encouragement from the core leadership, but nothing more.”

The movement’s global reach is also a study in how money buys influence, not that al-Qaeda’s paymasters are particularly fussy about whose loyalty they buy. Criminals and sectarian bigots with only limited interest in the movement’s wider global goals have taken their money, with appalling consequences in places like Iraq. At the height of al-Qaeda’s power there in early 2007, US soldiers showed The Sunday Telegraph a horrific “snuff DVD” produced by a Sunni insurgent named Omar the Slayer, which featured sectarian beheadings and bombings.

Correspondence seized along with the DVD suggested it had been sent as an effective “grant application” to a wealthy Saudi benefactor, who sent back several thousand dollars to buy weapons.

So what can be done? Borrowing from the terminology of computer software, Nato officials now talk of a “Counter-Terrorism 3.0”, focusing mainly on pre-emptive tactics to stop al-Qaeda taking root in the first place.

Yet to some extent, that strategy has already been tried. The US military’s 2,000-strong Horn of Africa Task Force, established in Gulf of Aden port of Djibouti in 2004, has precisely such a “hearts and minds” remit. With America and Europe already burdened with a fragile Iraq and an unravelling Afghanistan, capacity is also an issue. The most Yemen can expect from last week’s conference is extra aid money and some help in counter-terrorism. Somalia, with no functioning govermment at all, will struggle to get even that.

Meanwhile, although there is widespread agreement that the battleground lies as much in the mind as in the streets, mountains or deserts, debate remains as to whether Saudi-style rehab programmes are the right answer. Critics contend that the Prince Mohammed project’s softly-softly approach is simply a way for Saudi’s rulers to sweep dissent under the carpet, and that it is far too easy for inmates to simply pretend they have reformed. Its backers, though, say there is little alternative – punishment, after all, is a limited sanction against a movement that thrives on martyrdom.

Saudi officials maintain that only a tiny minority of the programme’s 120 former Guantanamo inmates are known to have reoffended – while the rest are, they claim, helping to combat the spread of al-Qaeda’s ideology. Defeating that, they point out, is the only sure route to vanquishing al-Qaeda permanently.

Yet even if it was an unqualified success, the Saudi scheme offers only a limited template for elsewhere. Undoubtedly, one of the reasons men like Mr Bawardi are persuaded to stay on the straight is its generous perks: since leaving, he has been given a free car, a £500 a month stipend, and a job with the Chamber of Commerce, giving him enough money to marry and settle down, and preventing a return of the boredom and loneliness that once drove him to jihad.

Such generosity would be totally unaffordable in Yemen or Somalia – and, most likely, politically unacceptable in Britain and many other countries.

All the same, nobody is more aware than the programme’s sponsors of the threat that al-Qaeda’s latest Yemen venture continues to pose, and the difficulty of identifying the genuinely contrite.

Last August, the programme’s chief patron, Prince Muhammad bin Nayef, was nearly killed when he granted a personal audience to would-be repenter who then detonated a suicide bomb of plastic explosive in his underwear. Four months later, the passengers of North West Airlines Flight 253 to Detroit had a similarly narrow escape.

But it may be only a question of time before someone else gets it right. And across the arc of terror there are still many more disaffected young men and women willing to give it a try.